test(e2e): fix auth specs for character routes

e2e/specs/mock/auth/logout-from-sidebar.spec.ts

@@ -5,8 +5,11 @@ import {
   clearBrowserState,
   defaultCharacterSidebarPath,
   defaultCharacterSplashPath,
+  defaultCharacterChatUrl,
+  enterChatFromSplash,
   getSplashStartChatButton,
-  signInWithEmailAndOpenChat,
+  submitEmailLogin,
+  switchToEmailSignIn,
 } from "@e2e/fixtures/test-helpers";
 
 test.beforeEach(async ({ baseURL, context, page }) => {
@@ -17,11 +20,19 @@ test.beforeEach(async ({ baseURL, context, page }) => {
 test("user can log out from the sidebar after email login", async ({
   page,
 }) => {
-  await signInWithEmailAndOpenChat(page);
+  await enterChatFromSplash(page);
+  await page
+    .getByRole("button", { name: "Sign up to unlock more features" })
+    .click();
+  await expect(page).toHaveURL(/\/auth(?:\?.*)?$/);
+  await switchToEmailSignIn(page);
+  await submitEmailLogin(page, { expectedUrl: defaultCharacterChatUrl });
   await expect(page.getByRole("button", { name: "Menu" })).toBeVisible();
 
   await page.getByRole("button", { name: "Menu" }).click();
-  await expect(page).toHaveURL(new RegExp(`${defaultCharacterSidebarPath}$`));
+  await expect(page).toHaveURL(
+    new RegExp(defaultCharacterSidebarPath.replace("?", "\\?") + "$"),
+  );
 
   const logoutRequestPromise = page.waitForRequest("**/api/auth/logout");
   await page.getByRole("button", { name: /Log out/i }).click();